Uniform boundedness principle

In mathematics, the uniform boundedness principle or Banach-Steinhaus Theorem is one of the fundamental results in functional analysis and, together with the Hahn-Banach theorem and the open mapping theorem, considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators whose domain is a Banach space, pointwise boundedness is equivalent to boundedness.

Related Topics:
Mathematics - Functional analysis - Hahn-Banach theorem - Open mapping theorem - Continuous linear operator

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The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus but it was also proven independently by Hans Hahn.

Related Topics:
1927 - Stefan Banach - Hugo Steinhaus - Hans Hahn

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